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Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

Measurements incompatible in quantum theory cannot be measured jointly in any other no-signaling theory

Michael Wolf, NBI Copenhagen

joint work with David Perez-Garcia, and Carlos Fernandez

"While [...] the wave function does not provide a complete description of physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.'' Einstein, Podolsky and Rosen, 1935.

More than seventy years after Einstein, Podolsky and Rosen (EPR) raised this puzzle we know, as a consequence of Bell's argument, that a complete theory in the sense of EPR would force us to pay a high price--- such as giving up Einstein locality. Could there, however, be a theory which provides more information than quantum mechanics but still is `incomplete enough' to circumvent such fundamental conflicts? In this work we address a particular instance of this question, in the context of which the answer is clearly negative: observables which are not jointly measurable within quantum mechanics must remain incompatible in every hypothetical refinement of this theory unless one gives up Einstein locality.

More technically speaking we show that the maximal Bell violation is the Lagrangiang dual of the joint measurability problem.